Аннотация:
Provability logic $\mathbf{GLP}$ is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of $\mathbf{GLP}$ interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of $\mathbf{GLP}$. We develop some constructions to build nontrivial GLP-spaces and show that $\mathbf{GLP}$ is complete w.r.t. the class of all GLP-spaces.

The first author was supported by the Russian Foundation for Basic Research (RFBR), Russian Presidential
Council for Support of Leading Scientific Schools, and the Swiss–Russian cooperation project
STCP-CH-RU “Computational proof theory”.
The second author was supported by the Shota Rustaveli National Science Foundation grant #FR/489/
5-105/11 and the French–Georgian grant CNRS–SRNSF #4135/05-01.